As Jordan Bowery – once the club’s record signing – had his contract terminated by mutual consent, Burke was arriving at the AESSEAL New York Stadium.
The Scottish international, who has joined on loan until the end of the season, is the second signing in as many days after the Millers completed a deal for striker Luciano Becchio on Thursday.
“Chris is a very experienced player and he knows the level,” said Redfearn.
“He has got that turn of pace, the ability to go past people to create and score.
“He adds good competition and he adds some real Championship quality that perhaps we have been lacking a little at times.
“He is a really good signing for us, he gives us balance on the right side which frees young Grant Ward up to play more centrally.
“That Championship experience will prove invaluable because we have got ourselves into a position when we are playing well, but we need to keep picking points up and start turning good performances away from home into results.
“The more experienced guys you have around the place to help the younger lads then the stronger you will become.”
Striker Bowery, 24, joined from Aston Villa in June 2014 but has netted just six goals at Rotherham. He has not featured for the Millers since November 3 and recently had a three-game loan spell at Bradford City.
Bowery yesterday completed a move to Oxford United.
The Millers today travel to Cardiff City today, looking to pull away from the relegation zone. They sit 21st, only avoiding the bottom three due to goal difference.